https://doi.org/10.1140/epjc/s10052-023-11270-y
Regular Article - Theoretical Physics
Effective action of a self-interacting scalar field on brane
1
Institute of Theoretical Physics and Research Center of Gravitation, Lanzhou University, 730000, Lanzhou, China
2
Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, 730000, Lanzhou, China
3
Joint Research Center for Physics, Lanzhou University and Qinghai Normal University, 730000, Lanzhou, China
Received:
3
November
2022
Accepted:
24
January
2023
Published online:
5
February
2023
In extra dimensional theories, the four-dimensional field theory is reduced from a fundamental field theory in the bulk spacetime by integrating the extra dimensional part. In this paper we investigate the effective action of a self-interacting scalar field on a brane in the five-dimensional thick braneworld scenario. We consider two typical thick brane solutions and obtain the Pöschl–Teller and harmonic potentials of the Kaluza–Klein (KK) modes, respectively. The analytical mass spectra and wave functions along extra dimension of the KK modes are obtained. Further, the effective coupling constant between different KK particles, cross section, and decay rate for some processes of the KK particles are related to the fundamental coupling in five dimensions and the new physics energy scale. Some interesting properties of these interactions are found with these calculations. The KK particles with higher mode have longer lifetime, and they almost do not interact with ordinary matter on the brane if their mode numbers are large enough. Thus, these KK particles with higher modes might be a candidate of dark matter.
© The Author(s) 2023
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